Fractal fatigue crack

ABSTRACT

The fractal dimension of a micrograph is a quantitative parameter of its geometric patterns' complexity, morphological irregularities and characteristics in their spatial arrangements and configurations. Material defects growing during fatigue process are described in terms of $\mathit{f}\mathit{r}\mathit{a}\mathit{c}\mathit{t}\mathit{a}\mathit{l}\mathit{s}$. The experimental assessment of fractal dimensions of the novel flaky electron fractographs comprising the 3D planar topography of branched secondary cracks with distinctively oriented striations' $\mathit{i}\mathit{s}\mathit{l}\mathit{a}\mathit{n}\mathit{d}\mathit{s}$ and tearing ridges' $\mathit{n}\mathit{e}\mathit{t}\mathit{w}\mathit{o}\mathit{r}\mathit{k}\mathit{s}$ on the ‘fatigue crack propagation area’ in three different Zr–Nb alloys have been carried out and correlated with their corresponding low cycle fatigue responses at different temperatures. Image texture analysis has also been implemented to understand the relative ‘energy generation’ of the hierarchical fatigue crack propagation during $\mathit{f}\mathit{a}\mathit{t}\mathit{i}\mathit{g}\mathit{u}\mathit{e}\mathit{-}\mathit{f}\mathit{r}\mathit{a}\mathit{c}\mathit{t}\mathit{u}\mathit{r}\mathit{e}$ process of these materials as a function of test temperature. The detail invasive fractal character and chaos of these crack/striations' $\mathit{i}\mathit{s}\mathit{l}\mathit{a}\mathit{n}\mathit{d}\mathit{s}$ and tearing ridge $\mathit{n}\mathit{e}\mathit{t}\mathit{w}\mathit{o}\mathit{r}\mathit{k}$ morphologies after $\mathit{f}\mathit{a}\mathit{t}\mathit{i}\mathit{g}\mathit{u}\mathit{e}\mathit{-}\mathit{f}\mathit{r}\mathit{a}\mathit{c}\mathit{t}\mathit{u}\mathit{r}\mathit{e}$ have been convincingly revealed.

KEYWORDS:

• Fractal dimension
• fatigue crack
• image texture
• Zr–Nb alloy
• striation

Acknowledgments

The insightful suggestions, interesting comments and strong recommendations about the manuscript by the anonymous reviewers are gratefully appreciated. The comments were very helpful in improving the paper quality.

Disclosure statement

The author declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Data accessibility statement

The data consist of experimental and analytical outputs that have been plotted in the figures in the manuscript. The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.